Just hanging around - part3

If the time period of SHM of rectangular block can be represented as \[T=2\pi \sqrt{\frac{m(\sqrt a +b)}{ck}}\]

Find the value of \(a+b+c\).

Details and Assumptions:

  • Treat the pulley as a disc.

  • The block and pulley are oscillating in the same phase with the same frequency.

  • Pulley has sufficient friction for Pure Rolling and mass=m & strings are light and inextensible.

  • Gravity is present.

  • Zig-zag lines in fig represents spring of spring constant \(k\) and \(2k\) as shown.

  • a is a square-free integer and the fraction is in simplest form.

Try its different variants - medium and easy

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